University of Guilan Journal of Algebra and Related Topics 2345-3931 5 1 2017 06 01 A Note on a graph associated to a commutative ring 61 82 2399 10.22124/jart.2017.2399 EN S. Visweswaran Saurashtra University J. Parejiya Saurashtra University Journal Article 2017 08 06 The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings.  In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rx\cap Ry = Rxy$.  In Section 2 of this article, we classify rings $R$ such that $G(R)$ is complete and we also consider the problem of determining rings $R$ such that $\chi(G(R)) = \omega(G(R))< \infty$. In Section 3 of this article, we classify rings $R$ such that $G(R)$ is planar.<br /><br /> https://jart.guilan.ac.ir/article_2399_1591422012d4680950f3bb1760b533a6.pdf